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fractint-digest       Friday, September 4 1998       Volume 01 : Number 288




----------------------------------------------------------------------

Date: Wed, 02 Sep 1998 22:14:39 -0600
From: Phil McRevis <[e-mail]>
Subject: (fractint) Re: fractals in postscript

[e-mail] (Wim de Lange)  writes:
> Some years ago there was an article in the Byte about postscript. And
> in this article there was an postscript program to calculate the
> mandelbrot set. Is there someone who has this article and/or the
> postscript program for this. I've now an postscript printer
> available, and I want to test this on the printer.

Its not that hard to do, but there are a couple reasons why you
probably don't want to compute M in PS:

o M is floating-point intensive and most PS printers aren't optimized
  for floating-point math.
o PS is interpreted and the burden of interpretation only adds to the
  already heavy computational burden of computing M.
o You'll probably get faster results by computing M in GIF format and
  converting the GIF image to PS and printing the image.

However, if you just want to see it run 'for yucks', try the following
postscript file on your printer:
<http://www.mit.edu:8001/afs/sipb.mit.edu/contrib/postscript/Color/mandelbrot_color.ps>

You may need to tweak the file in an editor to adjust the end-of-line
convention (postscript is ASCII and that file has the unix end-of-line
convention).
- --
http://www.xmission.com/~legalize/    Legalize Adulthood!
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Date: 03 Sep 98 07:46:02 GMT
From: [e-mail] (Wim de Lange)
Subject: (fractint) Re: fractals in postscript

Op  2 Sep 98 om 22:14 schreef Phil McRevis over: "Re: fractals in
postscript"

> Its not that hard to do, but there are a couple reasons why you
> probably don't want to compute M in PS:

I'm well aware of them I played many years with fractals, and wrote
little basic programs before I was aware of fractint and such stuff.
And long ago I had that article, and I found it 'funny' (not the
right word, my english is not good enough) that a printer has a
programming language that is capable of calculating the M-set.

> <http://www.mit.edu:8001/afs/sipb.mit.edu/contrib/postscript/Color/m
> andelbrot_color.ps>

I downloaded it.

> end-of-line convention (postscript is ASCII and that file has the
> unix end-of-line convention). --

No problem.


Groetjes,
    Wim de Lange
 _____________________________________

 Internet:    [e-mail]
 CompuServe:  100142,604
 _____________________________________


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Date: Thu, 3 Sep 1998 05:52:48 -0400
From: Sylvie Gallet <[e-mail]>
Subject: (fractint) Sylvie's site

Hi Christian,

>> I had problems though with accessing Gallet_c.zip, Gallet_d.zip and
>> wallpapr.zip and the vesa2cfg link. AOL answered with a simple 'URL
>> not found'.

  It was a problem with case sensitive filenames, it's fixed.

  Cheers,

        - Sylvie

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Date: Thu, 03 Sep 1998 06:55:58 -0500
From: Elaina Tillinghast <[e-mail]>
Subject: Re: (fractint) New Images on Web

Well a couple of things got in the way of me getting to my web pages...

The preferrence of what size image is most favored was split equally
down the middle between 640x480 and 1024x768. Either you want all to fit
on one screen quickly or you want all the detail you can get.

I thank all those people who took time to write. The results are in
favor of 640x480 since bigger would make it so many could not see them
at all. Then if space isn't a problem, BIG! as a choice for those who
can handle it.

Juice -have fun --harm none

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Date: Thu, 3 Sep 1998 13:43:39 +0100
From: Dave <[e-mail]>
Subject: (fractint) Posting fractal images on the web

I've noticed that many pages showing each fractal pattern tend to have
ALL images as huge GIFs on the title page.

Wouldn't it be a better idea to:

a) have thumbnails linking to the larger picture, so that you can browse
through ALL images from the title page and select the one you want to
see in full splendor
b) Store the larger versions as .JPEGs, thus permitting a full range of
colours but keeping the filesize of the images down. This allows the
images to be downloaded quickly, but I don't know what impact it has on
the overall quality of the picture
c) have perhaps two different links under each thumbnail, pointing to
640x480 or 1024x768-sized images, thus satisfying resolution
requirements of both parties. (But it'd mean reconstruction of each
image at different resolutions, or resizing/resampling in an imaging
package - is this feasible?)

I realise many people are still starting out in HTML, and fall into the
pitfall of not realising that what appears instantly when browsed
locally takes much longer when viewed via a modem. As a test, try
flushing your web browser cache and then view your pages via your ISP to
see how long they take to come down.

Any views on this, people?
> ----------
> From:     Elaina Tillinghast[SMTP:[e-mail]]
> Reply To:     [e-mail]
> Sent:     03 September 1998 12:55
> To:     [e-mail]
> Subject:     Re: (fractint) New Images on Web
>
> Well a couple of things got in the way of me getting to my web
> pages...
>
> The preferrence of what size image is most favored was split equally
> down the middle between 640x480 and 1024x768. Either you want all to
> fit
> on one screen quickly or you want all the detail you can get.
>
> I thank all those people who took time to write. The results are in
> favor of 640x480 since bigger would make it so many could not see them
> at all. Then if space isn't a problem, BIG! as a choice for those who
> can handle it.
>
> Juice -have fun --harm none
>
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> Post Message:   [e-mail]
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> Unsubscribe:    [e-mail] "unsubscribe fractint"
>

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------------------------------

Date: Thu, 03 Sep 1998 08:08:26 -0700
From: "Angela Wilczynski" <[e-mail]>
Subject: Re: (fractint) Posting fractal images on the web

Dave wrote:
>
> I've noticed that many pages showing each fractal pattern tend to have
> ALL images as huge GIFs on the title page.
>
> Wouldn't it be a better idea to:
>
> a) have thumbnails linking to the larger picture, so that you can browse
> through ALL images from the title page and select the one you want to
> see in full splendor

For some of us with many fractals on display, even thumbnails of ALL the
images create an introductory page that is too slow to download. I am a
very firm believer in paying great attention to bandwidth, particularly
on the introductory page.  Most surfers will go on to something else if
the intro page doesn't show it's stuff in less than a minute.
Fortunately, not everything need be displayed at once....only enough
material to pique interest.

> b) Store the larger versions as .JPEGs, thus permitting a full range of
> colours but keeping the filesize of the images down. This allows the
> images to be downloaded quickly, but I don't know what impact it has on
> the overall quality of the picture

Storing Fractint images as jpgs destroys the information that is bundled
with the image and which can be used after the gif is downloaded and
opened in Fractint. So moving to jpg is, for me, a matter of deciding
which audience I want to please most....the one with limited time or
patience or my Fractint collegues. Also, I find conversion from gif to
jpg is sometimes unsatisfying in terms of how the image looks.

> c) have perhaps two different links under each thumbnail, pointing to
> 640x480 or 1024x768-sized images, thus satisfying resolution
> requirements of both parties. (But it'd mean reconstruction of each
> image at different resolutions, or resizing/resampling in an imaging
> package - is this feasible?)
>

This is basically a lot of work and assumes one has a great deal of
space available and can choose to store the same image twice. A more
practical solution is one many on the list use......provide the image as
a jpg and as a par file.

Angela

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------------------------------

Date: Thu, 3 Sep 1998 11:08:41 EDT
From: [e-mail]
Subject: Re: (fractint) Understanding Formulas

In a message dated 02-09-98 3:41:05 PM EST, [e-mail] writes:

<< I've been experimenting with formulas and pars done by those on the list
 and ones that I've found here and there for several weeks now.
 Something that has been intriguing me is how do people come up with the
 formulas and coloring methods that they do?
  >>
Ken,
If you want some good starting places pick up a Calculus and Analytical
Geometry book at a library or flea market.  As you go through it you'll find
lots of equations to plug into an escape type fractal.  If you look at
'series' their convergence and divergence and what separates the two and
remainder theory it'll give you more ideas.  Then the next book you could look
for is one on comnplex analysis and conformal mapping.  things are very
different in the complex plane.

I'm relatively new to the IF...ENDIF logic and I haven't done much with it.
This tool gives you precision control over the coloring method but a lot of
mathematical up front work is required.  As a basic rule of thumb when you
iterate you can track   three basic values: the count at which you are at, the
value which you are at, and the location in your coordinate system (cartesian,
polar, etc).  by establishing standards of comparison for those values you
have come up with a new unique coloring /rendering method.  Unfortunately its
been my experience that to rigorous a standard makes your fractals look plain
and lousy.  Always be willing to test your standards boundry because thats
where it gets great.

for instance (off the top of my head) say we want to test our iteration based
on count and value so that as count increases we begin to loose grasp of the
original value(kind of like hiesenberg).  z=current value   n= iteration count
c=arbitrary constant:
conditional test: |z|<= (c+z/n)^n

try the conditional >=
     (half the time things get exciting around zero the other half infinity)
change the arbitrary constant to extremes
make n a function of iteration n=F(iter#)
etc.
Can I begin to see where this is going. NO!  but I'm pretty familiar with how
the M-set behaves so I'll iterate that function with this test first and see
what it does to the that behavior.

Try halley maps in regions that f'(z)>f(z) (divergent areas).
Try halley maps on functions with singularities or discontinuity

And best of all, it can turn out to be just junk or it could be a surprise.

I hope this helps. This thought process is chaotic like my explanation.

Good luck
Rui




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------------------------------

Date: Thu, 03 Sep 1998 10:49:37 -0500
From: "Damien M. Jones" <[e-mail]>
Subject: Re: (fractint) Posting fractal images on the web

[Reply to Angela is below this one.]

Dave,

 - a) have thumbnails linking to the larger picture, so that you can browse
 - through ALL images from the title page and select the one you want to
 - see in full splendor

Yes, but this is still not an optimal solution if you have a lot of
pictures.  Right now I've got two layers of thumbnails before you get to
the actual pictures.  Few people want to download a page with 200+
thumbnails on it.

 - c) have perhaps two different links under each thumbnail, pointing to
 - 640x480 or 1024x768-sized images, thus satisfying resolution
 - requirements of both parties. (But it'd mean reconstruction of each
 - image at different resolutions, or resizing/resampling in an imaging
 - package - is this feasible?)

It does indeed mean resizing the images more than once, but if you're
preparing thumbnails, you're already preparing more than one size.  For
example, I typically generate my images at 1600x1200 or 1280x960; these are
then resized down to 640x480 and saved (large size), resized to 128x96 and
saved (thumbnail), and a few resized to 200x150 and saved (larger thumbnail
for the main gallery index).  I *could* have also prepared 1024x768
versions of these images, but when I started my gallery space was a
concern; space is no longer a problem for me, but the sheer quantity of
images *is*.  I'm not sure I want to take the time to prepare 1024x768
versions of so many pictures.

 - Any views on this, people?

Don't get me started. :-)

Angela,

 - Storing Fractint images as jpgs destroys the information that is bundled
 - with the image and which can be used after the gif is downloaded and
 - opened in Fractint.

This may or may not be a drawback, depending on your viewpoint.
Personally, I'd say go for the JPEG anyway, and provide a PAR file for
those that want parameters.  It's usually worth the savings.

 - Also, I find conversion from gif to jpg is sometimes unsatisfying in
 - terms of how the image looks.

Well, you *know* I'm going to say that doesn't have to be the case. :)
Generate your image at large size and reduce it (for anti-aliasing) and
then save in JPEG format with appropriate settings.

 - This is basically a lot of work and assumes one has a great deal of
 - space available and can choose to store the same image twice. A more
 - practical solution is one many on the list use......provide the image as
 - a jpg and as a par file.

And although I just advocated the JPEG+PAR approach, there are situations
where it isn't appropriate--particularly, cases where the image has been
post-processed in some fashion outside of FractInt, or produced with a
custom program that isn't generally available.  Or cases where you really
don't feel like giving out the PAR file. :-)

Damien M. Jones   \\
[e-mail]  \\  Fractalus Galleries & Info:
                    \\  http://www.fractalus.com/

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Date: Thu, 03 Sep 1998 12:32:17 -0500
From: "Damien M. Jones" <[e-mail]>
Subject: (fractint) Just two days left!

Greetings listfolk,

There are just two days left for you to submit your entries to the Fractal
Art '98 Contest.  Scores of entries have already been received; we
certainly appreciate the number of entries (more than last year's contest!)
and the exceptional quality and variety.

If you have not already submitted three images, the deadline is fast
approaching--no further entries will be accepted after 10PM PDT, September
5.  (That's Saturday night!)  We'd certainly like you to enter!  You can
find all the details--rules, categories, and so on--at the contest web site:

    http://www.fractalus.com/contest98/

Damien M. Jones   \\
[e-mail]  \\  Fractalus Galleries & Info:
                    \\  http://www.fractalus.com/

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Date: Thu, 3 Sep 1998 18:20:42 +0100
From: Dave <[e-mail]>
Subject: RE: (fractint) Posting fractal images on the web

> For some of us with many fractals on display, even thumbnails of ALL
> the
> images create an introductory page that is too slow to download.
Ah - crossed wires here. I looked at one webpage last week that had
about 6 full-sized pictures on it. I just thought it would have been a
better idea to reduce these to thumbs, thus getting a summary of what to
expect downloaded quickly. I didn't mean that I wanted everyone to fill
their title pages with thumbs of ALL of their current images!! But for
those with many fractals on display, surely thumbnails of them on an
intgro page is quicker to download than a page containing all of the
displays?
>  I am a
> very firm believer in paying great attention to bandwidth,
> particularly
> on the introductory page.  Most surfers will go on to something else
> if
> the intro page doesn't show it's stuff in less than a minute.
> Fortunately, not everything need be displayed at once....only enough
> material to pique interest.
Agreed. Perhaps categories of thumbs from an index page, etc....

> > b) Store the larger versions as .JPEGs, thus permitting a full range
> of
> > colours but keeping the filesize of the images down. This allows the
> > images to be downloaded quickly, but I don't know what impact it has
> on
> > the overall quality of the picture
>
> Storing Fractint images as jpgs destroys the information that is
> bundled
> with the image and which can be used after the gif is downloaded and
> opened in Fractint. So moving to jpg is, for me, a matter of deciding
> which audience I want to please most....the one with limited time or
> patience or my Fractint collegues. Also, I find conversion from gif to
> jpg is sometimes unsatisfying in terms of how the image looks.
>
    .. but surely your fract colleagues would prefer the formulae
with which you created the image, rather than reverse-engineer the GIF?
I'm still new to this game, but I had problems extracting image info
from a GIF I was given.
> > c) have perhaps two different links under each thumbnail, pointing
> to
> > 640x480 or 1024x768-sized images, thus satisfying resolution
> > requirements of both parties. (But it'd mean reconstruction of each
> > image at different resolutions, or resizing/resampling in an imaging
> > package - is this feasible?)
> >
>
> This is basically a lot of work and assumes one has a great deal of
> space available and can choose to store the same image twice. A more
> practical solution is one many on the list use......provide the image
> as
> a jpg and as a par file.
True, but I'm looking at it from the point of view that "the more effort
put in by the one writer, the less effort required by the many readers".
Perhaps it's a selfish view, I don't know. As for the space available,
the JPEG+PAR solution sounds a much better idea. Would two JPEGs of the
same image require less storage space than one GIF?



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Date: Thu, 03 Sep 1998 20:48:48 -0700
From: "Angela Wilczynski" <[e-mail]>
Subject: Re: (fractint) Posting fractal images on the web

Dave wrote:
> >
>         .. but surely your fract colleagues would prefer the formulae
> with which you created the image, rather than reverse-engineer the GIF?
> I'm still new to this game, but I had problems extracting image info
> from a GIF I was given.

> > This is basically a lot of work and assumes one has a great deal of
> > space available and can choose to store the same image twice. A more
> > practical solution is one many on the list use......provide the image
> > as
> > a jpg and as a par file.
> True, but I'm looking at it from the point of view that "the more effort
> put in by the one writer, the less effort required by the many readers".
> Perhaps it's a selfish view, I don't know. As for the space available,
> the JPEG+PAR solution sounds a much better idea. Would two JPEGs of the
> same image require less storage space than one GIF?


Let's see......

1.  Regarding the gif versus jpg question........I believe that I am
often doing everyone a favor by posting a largish gif with the Fractint
info in tact rather than the par (or at least in addition to the par)
because the par could take faaaaaaaaaaar longer to generate than the gif
does to download. That is always a consideration for me.  In general I
like the jpg + par approach because I feel more comfortable that my
images will be treated with care by my Fractint bretheren.  I figure the
jpg's....regardless of the copyright babble......will be pilfered.  That
is certainly another consideration in how I post my images......I give
up the really good stuff to the web with great reluctance.

2.  Dealing with the gif in fractint is simplicity itself.....put the
gif where you can reasonably locate it...the most basic spot being where
fractint resides....open the gif using "r" then save the parameters by
hitting that old "b".  You can zoom into or out of the fractal at will
right from the gif or use Paul Carlson's great hint of hitting z for the
parameters, then F6 and enter a couple of times. I hope I have that
right as I haven't done it in a while.  At any rate.....you can return
to the "original" image using the gif parameters in that way then start
on your own journey.  That is my fav thing to do.

3.  Space limitations are space limitations...period. If one doesn't
have space available to post (and most don't) the dual posting is not an
option. I consider my time  and space far more valuable than that of web
surfers who are a non-paying audience which MUST be considered because
"their" download minutes will cause them annoyance......I refuse to cost
myself hours of effort or more $$ for web space for their minor
inconvenience when they are getting a freebie. One is not required to
pander to all wishes. I try to make reasonable compromises.  I have in
excess of 35 megs of "stuff" on the web so managing it takes
considerable time already. Maybe those whose jobs are connected with the
web or who have smaller websites can more profitably use your
suggestions.

Angela

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Date: Thu, 03 Sep 1998 22:13:19 -0700
From: kathy roth <[e-mail]>
Subject: (fractint) Understanding Formulas

Hi math-ophiles.  This discussion has been very
interesting.  I have been clumping around getting
some understanding of the basics and am getting an
appreciation for the leap of thought it takes to think
of something new,  not so much how you write the
formula but the imagination in thinking of the orbit traps,
stalks and the flexballs, bubbles and triangles and all that.  It's
very creative.  I was reading about Julia and Fatou.
Early in this century they visualized all this (or a good part
of this) and never lived to see it on a screen and certainly
not in 256 colors.  I wonder if it was totally an
abstraction or if they could visualize it somewhat.
They never knew what it looked like or saw all these people
developing things from it.  (or.....who knows....)
          Anyway, I have some basic questions that I have
not been able to figure out using the references from this
list.  Some of it is math but I think more of it is programming
or just knowing the conventions of the If..Else formulas.
I've read (partially!) the Devaney and Peitgen books and some
things on chaos etc. and am at roughly an advanced high school
or college math for non-math major sort of level.
    Ummm, so-
basic math question on popcorn_jul and complex numbers:

Popcorn_Jul
   popcorn_jul { ; Paul Carlson, 1998
    ; Always use float=yes
    ;
    ; real(p1) = h in popcorn formula
    ; imag(p1) = bailout value
    ;
    x = real(pixel)
    y = imag(pixel)
    h = real(p1)
    :
    prev_x = x
    x = x - h * sin(y + tan(3 * y))
    y = y - h * sin(prev_x + tan(3 * prev_x))
    z = x + flip(y)
    |z| <= imag(p1)
}
I thought this was about separating the
x and y pixel in the initialization and then iterating
the Julia formula.  But does
    x = x - h * sin(y + tan(3 * y))
    y = y - h * sin(prev_x + tan(3 * prev_x))
have something to do with z^2 + c?

I thought I could figure this out with the
"Formulae for Complex Numbers" but
couldn't.  (Actually I do not get for example
why e^z=e^x(cosy + i*siny).  Would this be in an
Analytical Geometry text?)

Similarly, I always liked conic sections and graphs
in school and was looking at Kerry Mitchell's
conic section formulas.


conic { ; Kerry Mitchell 12may98
;
;       draws conic sections, not fractals
;          Ax^2 + Bx + Cy^2 + Dy + Exy + F = 0
;       A=real(p1), B=imag(p1), C=real(p2), D=imag(p2)
;       E=real(p3), E=imag(p3).  use decomp=256 coloring
;
        a=real(p1), b=imag(p1), c=real(p2), d=imag(p2)
        e=real(p3), f=imag(p3), iter=-1:
        x=real(pixel), y=imag(pixel)
        t=x*(a*x+b)+y*(c*y+d)+e*x*y+f
        t=log(cabs(t))
        z=cos(t)+flip(sin(t))
        iter>0
        }

I understand the Ax^2 + Bx parts.  Where did
the
" t=log(cabs(t))
        z=cos(t)+flip(sin(t))"      come from?

Thanks!  Sorry about the length of this-  Kathy






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Date: Thu, 03 Sep 1998 22:35:05 -0700
From: kathy roth <[e-mail]>
Subject: (fractint) Understanding Formulas

More formula questions!  I think I understand the
basics of the If..Else tutorial and understand
bailout.  But the If..Else formulas have phrases like:

"bailout == 0  && |w| < 4"

Bailout isn't actally 0, this seems like a language
that I don't know.


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Date: Tue, 01 Sep 1998 14:32:17 +0200
From: Guy Marson <[e-mail]>
Subject: Re: (fractint) Fractal Risks?

Hi Albert,

At 11:22 31.08.1998 -0400, you wrote:

>I am also interested in Amateur Radio,

    enjoy FRACTINT, it's a good antenna to the soul!

>drawing, painting and carving.
>I am 71 and am really starting to enjoy life.  Keep up the good
>work.      Albert
>


73's from LX1GM,

Guy



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Date: Fri, 4 Sep 1998 00:21:15 -0700 (MST)
From: Kerry Mitchell <[e-mail]>
Subject: Re: (fractint) Understanding Formulas

On Thu, 3 Sep 1998, kathy roth wrote:

>     Ummm, so-
> basic math question on popcorn_jul and complex numbers:
>
> Popcorn_Jul
>    popcorn_jul { ; Paul Carlson, 1998
    [snippage]
>     x = real(pixel)
>     y = imag(pixel)
>     h = real(p1)
>     :
>     prev_x = x
>     x = x - h * sin(y + tan(3 * y))
>     y = y - h * sin(prev_x + tan(3 * prev_x))
>     z = x + flip(y)
>     |z| <= imag(p1)
> }
> I thought this was about separating the
> x and y pixel in the initialization and then iterating
> the Julia formula.  But does
>     x = x - h * sin(y + tan(3 * y))
>     y = y - h * sin(prev_x + tan(3 * prev_x))
> have something to do with z^2 + c?

Paul is separating x and y and iterating them independently.  However,
this is *not* the familiar z^2+c formula.  That would look like this:

    x = x*x - y*y + real(c)
    y = 2*prev_x*y + imag(c)

Where the "prev_x" variable is used to force the y equation to use the
previous iteration's value of x, instead of the newly computed one in the
x formula.  I don't know if Paul's Popcorn formula has an easy expression
in terms of z.  If it did, he'd probably use it.

> couldn't.  (Actually I do not get for example
> why e^z=e^x(cosy + i*siny).  Would this be in an
> Analytical Geometry text?)

This should be easily found in a complex analysis text.  Basically, for
any angle theta,

    exp(i*theta) = cos(theta) + i*sin(theta).

*Why* this is depends on whose perspective you take, so it might just be
easier right now to accept it.  Then,

    exp(z) = exp(x+i*y) = exp(x)*exp(i*y) =
    exp(x)*[cos(y) + i*sin(y)].

This comes about from the rules of exponents (a^(b+c) = a^b * a^c) and the
exp(i*theta) expression above.

> Similarly, I always liked conic sections and graphs
> in school and was looking at Kerry Mitchell's
> conic section formulas.
    [more snippage]
> I understand the Ax^2 + Bx parts.  Where did
> the
> " t=log(cabs(t))
>         z=cos(t)+flip(sin(t))"      come from?

Two parts:  first, I use "t" as a temporary variable to hold the result
of the conic section calculation.  If t=0, then the iterate is right on
the section.  Since that will not happen very often, I want to highlight
those points "close" to the section, to show where it is.  I often do that
by using a log transform:  log(t) goes to negative infinity very quickly
as t goes to zero (from above, through postive numbers.  Use the cabs(t)
to make sure that the argument is positive, since I don't want imaginary
numbers at this point).  Part 2 is to use this transformed t as an angle.

    z = cos(t) + flip(sin(t)) is the same as
    z = cos(t) + i*sin(t), or
    z = exp(i*t).

So, when I use Fractint's "decomp=256" coloring, that will show
narrower and narrower bands of color as the (original) t goes to zero, or
as the iterate gets closer to the section.  Simple, right?  :-)

Anyway, you now have a little bigger window into my twisted world of
coloring scheme development, and hopefully, a little better understanding
of the math and programming behind them.

Kerry Mitchell

- -------------------------------------------------------------------------------
Kerry Mitchell   [e-mail]   www.primenet.com/~lkmitch/
- -------------------------------------------------------------------------------



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Date: Fri, 4 Sep 1998 00:26:30 -0700 (MST)
From: Kerry Mitchell <[e-mail]>
Subject: Re: (fractint) Understanding Formulas

On Thu, 3 Sep 1998, kathy roth wrote:

> More formula questions!  I think I understand the
> basics of the If..Else tutorial and understand
> bailout.  But the If..Else formulas have phrases like:
>
> "bailout == 0  && |w| < 4"

This means, "bailout equals 0 and magnitude of w is less than 4".  The
"==" means "is it equal to?", as opposed to "=", which means, "set it
equal to".  "&&" means "and", but the Boolean kind, where if the statement
"a && b" is true, then both "a" and "b" have to be true.  The Boolean "or"
is "||".  The rest is fairly standard formual stuff--checking the
magnitude of a complex number to see if it's smaller than some threshold.

Kerry Mitchell



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Date: Fri, 4 Sep 1998 10:19:03 -0400 (EDT)
From: [e-mail] (Kragen)
Subject: Re: (fractint) Understanding Formulas

On Fri, 4 Sep 1998, Kerry Mitchell wrote:
> On Thu, 3 Sep 1998, kathy roth wrote:
> > "bailout == 0  && |w| < 4"
>
> This means, "bailout equals 0 and magnitude of w is less than 4".  The

I'm confused.  I thought |w| meant the square of the magnitude of w,
not the magnitude of w itself.

Kragen (a formula newbie)

- --
<[e-mail]>       Kragen Sitaker     <http://www.pobox.com/~kragen/>
I don't do .INI, .BAT, .DLL or .SYS files. I don't assign apps to files. I
don't configure peripherals or networks before using them. I have a computer
to do all that. I have a Macintosh, not a hobby. -- Fritz Anderson


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Date: Fri, 4 Sep 1998 07:22:34 -0700 (MST)
From: Kerry Mitchell <[e-mail]>
Subject: Re: (fractint) Understanding Formulas

You're right.  My bad.  Thanks.

- -------------------------------------------------------------------------------
Kerry Mitchell
[e-mail]
www.primenet.com/~lkmitch/
- -------------------------------------------------------------------------------

On Fri, 4 Sep 1998, Kragen wrote:

> On Fri, 4 Sep 1998, Kerry Mitchell wrote:
> > On Thu, 3 Sep 1998, kathy roth wrote:
> > > "bailout == 0  && |w| < 4"
> >
> > This means, "bailout equals 0 and magnitude of w is less than 4".  The
>
> I'm confused.  I thought |w| meant the square of the magnitude of w,
> not the magnitude of w itself.
>
> Kragen (a formula newbie)
>
> --
> <[e-mail]>       Kragen Sitaker     <http://www.pobox.com/~kragen/>
> I don't do .INI, .BAT, .DLL or .SYS files. I don't assign apps to files. I
> don't configure peripherals or networks before using them. I have a computer
> to do all that. I have a Macintosh, not a hobby. -- Fritz Anderson
>
>
> --------------------------------------------------------------
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>


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Date: Fri, 4 Sep 1998 12:23:46 -0400
From: "Marie Drozdis" <[e-mail]>
Subject: RE: (fractint) Understanding Formulas

Please don't use this list to start a platform war.

Thank you.

- -----Original Message-----
From:    [e-mail]
[mailto:[e-mail]] On Behalf Of Kragen
Sent:    Friday, September 04, 1998 10:19 AM
To:    [e-mail]
Subject:    Re: (fractint) Understanding Formulas

<[e-mail]>       Kragen Sitaker     <http://www.pobox.com/~kragen/>
I don't do .INI, .BAT, .DLL or .SYS files. I don't assign apps to files. I
don't configure peripherals or networks before using them. I have a computer
to do all that. I have a Macintosh, not a hobby. -- Fritz Anderson



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Date: Fri, 04 Sep 1998 13:04:11 -0400
From: Diosnel Herrnsdorf <[e-mail]>
Subject: Re: (fractint) Understanding Formulas

> (Actually I do not get for example
> why e^z=e^x(cosy + i*siny).  Would this be in an
> Analytical Geometry text?)

Hi, Kathy.
I don't think I'm able to give an answer for most of your questions.
However, I'll give you this one.
First of all, remember that z=x+i*y, where i=sqrt(-1). Now, you can
write e^z=e^(x+i*y)=e^x*e^(i*y). The first part of the product comes
into the formula.
The second part comes from Euler's identity: e^(i*y)=cosy+i*siny. You
can reach it with Taylor's series. If you express cosy, i*siny and
e^(i*y) as series, you will get the identity.
You see that the answer is more in calculus than in analytical geometry,
though I think there should be some little explanation in the
preliminars of complex numbers.
I hope this is not too dark (this is the first time I'm thinking math in
English) and helps you understand it a little.:-)
Regards,
Diosnel


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End of fractint-digest V1 #288
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